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Design of one dimensional refractive index sensor using ternary photonic crystal waveguide for plasma blood samples applications
Physica E: Low-dimensional Systems and Nanostructures 111 (2019) 29–36
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Physica E: Low-dimensional Systems and Nanostructures journal homepage: www.elsevier.com/locate/physe
Design of one dimensional refractive index sensor using ternary photonic crystal waveguide for plasma blood samples applications
T
Hala J. El-Khozondara, P. Mahalakshmib, Rifa J. El-Khozondarc, N.R. Ramanujamd, I.S. Amirie,f,∗, P. Yupapine a
Electrical Engineering Department, Islamic University of Gaza, Gaza, Palestine Department of Electronics and Communication, Vaigai College of Engineering, Madurai, 625 122, India c Physics Department, Al-Aqsa University, Gaza, Palestine d Department of Physics, K.L.N. College of Engineering, Pottapalayam, 630 612, India e Computational Optics Research Group, Advanced Institute of Materials Science, Ton Duc Thang University, Ho Chi Minh City, Viet Nam f Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Viet Nam b
A R T I C LE I N FO
A B S T R A C T
Keywords: Ternary PC Graphene Sensor Transfer matrix method (TMM)
One dimensional ternary photonic crystal based refractive index sensor is numerically proposed for the blood plasma sensing applications. It is achieved by introducing the defects or cavity cell, where the blood samples are infiltrated and surrounded by the graphene layers at the middle region of the ternary structures. Introduction of the graphene layer is to avoid the change in blood sample characteristics due to few ambient factors. The whole structure is then tuned to observe the transmittance spectrum over the infrared region (800 nm–1200 nm). It is noticed that the resonance spectral shift occurs for variation of the blood plasma samples as 10 g/l, 20 g/l, 30 g/l, 40 g/l & 50 g/l. These spectral shifts report the device sensitivity and it is optimized for different filling factor of nanocomposite material and different thickness of the graphene coating.
1. Introduction Optical sensors are important devices that detect and predict the signal changes in certain environments. They are useful in different applications, particularly, in industry and medicine. Their sensitivity depend on different factors including the type of materials, thickness of the film, and angle of incidence [1–4]. In earlier days, the properties of transfer matrix method (TMM) were investigated for different multilayered structures. It has been stacked and segmented as a different region by owning its refractive index which was also composited as one dimensional homogeneous multilayered thin film. In the case of structural formation with mirroring regions, the incident electromagnetic wave (EM) at a specific incidence angle hits the interface region and travels along the same stacked structure with the veneration of the materials properties. By 1950, the optical propagation characteristics of multilayered periodic region were evolved by using TMM [5]. Later it was verified by Hooke [6] and Newton et al. [7] during the pulse propagation in periodic multilayered regions with high dense of transmittance and reflectance over the band gap region which might be in visible, infrared, or mid-infrared regions [8]. Further, in order to tune up the efficient optical transmission characteristics, the
∗
composition of periodic multilayered structural pattern between the dielectric or any combination of materials was explored, where it is known as photonic crystal's (PCs) [9,10] which was also distended for 2D & 3D along with 1D [11–16]. The exertion of 1D-PC was proclaimed for the low intense of reflectivity by generating modes or photons as bands, where the region of zero propagation level for the periodic crystalline structure called as photonic band gap (PBG). Regardless the material composition and structural perfection, as the manipulation of the optical light can control the penetration, the photonic band gap analysis was extensively used in various applications and this features some fundamental physical studies such as filter applications especially for narrowband filter [17], bandpass filter [18], polarization controller [19], switching [20] and sensing applications [21,22]. Later it was inferred that the PBG effect also affectionate and enhancing the change of materials as well as the different structural module. In material aspects, PC's pulse propagation has been prolonged and proven in all kinds of dielectric region, nanocomposites region, plasma layer region [23–26] and superconductivity region [27]. Similarly, the band of the energy PCs response in its transmission and reflection spectrum for various structures, fibonacci quasi-periodic [28,29], graded multi-structure [30], thuemorse [31] and ternary structures [32]. In addition, the
Corresponding author. Ton Duc Thang University, Ho Chi Minh City, Viet Nam. E-mail address: [email protected] (I.S. Amiri).
https://doi.org/10.1016/j.physe.2019.02.030 Received 6 January 2019; Received in revised form 21 February 2019; Accepted 25 February 2019 Available online 28 February 2019 1386-9477/ © 2019 Elsevier B.V. All rights reserved.
Physica E: Low-dimensional Systems and Nanostructures 111 (2019) 29–36
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ternary based multilayer structures have some greater impacts on multi material composition properties for multi-applications especially it paid attention on sensing properties. Few researchers have been doing research on sensing in one dimensional [33] and two dimensional [34] PCs. More recently, researcher are fascinated by ternary photonic crystals due to their superior performance over one-dimensional periodic binary crystals in omni directional reflection [35], tunable optical filtering [36] and sensing applications [37]. In addition, the ternary structures are used for sensing application by forming the defect region [38] at the middle of the multilayered structure. Recently, JijiangWu et al. [39] proposed a temperature sensor using ternary structure in which one of the layers is superconductor material, where the sensor has reported sensitivity of 31.18 nm/K. In 2018, PCs had also been used for sensing devices in biomedical applications by Ramanujam et al. who proposed the refractive index sensor device for cancer cell by introducing defect layer with the exertion of mode function in the band gap region, where the device sensitivity was 43 nm/RIU [40]. In this article, the ternary based 1D photonic crystal is proposed for blood plasma sensing applications, where the sensing properties are tuned by adjusting the filling factor of the nanocomposites and the thickness of the graphene layers surrounded at both side region of the defective layer. In sensor development process, TMM is the time-saving in calculation and structure optimization. It can be also used for quickly design and optimizing the structure parameters. Next section is devoted to the design and theoretical background. Section 3 is dedicated to results and discussion followed by conclusion.
εAg = ε∞ −
εAg − εc εB − εc =f εB − 2εc εAg − 2εc
(2)
(3)
where, f is the Ag filling factor [45]. The period of the lattice is fixed as d = dA + dB + dC = 100 + 45 + 100 = 245 nm . The refractive index of the defected plasma in blood compound with the following formula
nD = 1.32459 + 0.001942Cp
(4)
where, Cp is the plasma concentration in blood and is measured in terms of g/l. In this calculation, Cp varies from 0 g/l to 50 g/l in steps of 10 g/l and its corresponding refractive index (nD) is calculated as 1.32459 to 1.42169. Since the graphene layers produce the low absorption at low frequency region and enhance the optical propagation characteristics in the infrared region, the defect layer is sandwiched in between the graphene nanolayers. It is due to influence the compact sensing properties during the process of variation of blood samples in g/l. The Graphene layer labeled as G has thickness dG and refractive index nG = εG with [46]
εG = 1 + j
σ (ω) ε0 ωd G
(5)
where, ε0 is the permittivity in the vacuum. σ(ω), the surface conductivity of graphene, equals σintra(ω) + σinter(ω), where σintra(ω)and σinter(ω) are intraband conductivity and the interband conductivity and is represented in the following expression
A 1-D ternary PC with defective layer is designed for detecting the plasma blood samples in the given blood analytes. As presented in Fig. 1, the proposed structure is Air/(SnS/Nanocomposite/SiO2)N/ Graphene/D/Graphene/(SnS/Nanocomposite/SiO2)N/Air. D is the defect layer to be filled with blood sample and the number of periods N is considered here as 5. Tin sulfide (SnS) is chosen as high-refractiveindex material with low transmittance in the optical frequency range of 500 nm to 3000 nm, where the SiO2 has been chosen as the low-refractive-index material and experimentally compact to form the thin layered film. The same SiO2 material is composited with silver nanoparticle by Maxwell garnett approximation to form the Nanocomposite material, which can be used to enhance the sensitivity in the given optical range. Further, the SnS layer thickness is dA = 100 nm, where its refractive index as nA is 2.6 [41]. The thickness and refractive index of the SiO2 layers are dC = 100 nm and nC = εC respectively and
0.61497λ2 − λ2c22 λ2 − c12
+ jωυp2
where, ω is the angular frequency, ωp is the selected plasma frequency which is taken as 9 eV, υp is the plasma collision frequency = 0.02eV and ε∞ is the permittivity at infinite frequencies (=5 for Ag). The Nanocomposite layer with thickness dB = 45 nm has effective index nB = εB where εB can be found from equation (3),
2. Design and theoretical background
εc = 1.4923 +
ωp2 ω2
σintra (ω) = −j
μc e 2kB T ⎛ μc + 2 ln ⎛e − kB T + 1⎞ ⎞⎟ ⎜ π ħ2 (ω − j Γ) ⎝ kB T ⎝ ⎠⎠
(6)
σinter (ω) = −j
2μ − (ω − j Γ)ħ ⎞ e2 ln ⎛⎜ c ⎟ 4π ħ ⎝ 2μc + (ω − j Γ)ħ ⎠
(7)
Where, e is the charge of an electron, μc is the chemical potential, Γ is the phenomenological scattering rate, T is the Kelvin temperature, kB is Boltzmann's constant, ħ = h/2π is the reduced Planck's constant. The graphene thickness dG is allowed to vary for the sack of optimizing the sensor characteristics. The overall sensing performance is numerically simulated for the proposed structure for the TE mode propagation in the infrared region. For the TE modes, transfer matrix method (TMM) is used to study the interaction of light through the structural penetration of photonic crystal in the optical region and it also could be possible for experimental validation while following the one dimensional multilayer practical measurement [47–49]. For the periodic layer i, the matrix Mi describe the propagation of
(1) −2
and λ is the wavelength where, C1 = 0.115 μm, C2 = 0.01059 μm [42]. For unmagnetized plasma, the frequency dependent dielectric permittivity for silver (εAg) meets the Drude model and it can be written as [43,44]:
Fig. 1. The proposed 1-D ternary PC sensor. 30
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Fig. 2. The transmittance power as a function of λ for cp = 0 g/l at different values of f as indicated.
Fig. 3. The transmittance power as a function of λ for different values of cp (g/l) as color indicates at f = 0. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
Fig. 4. The transmittance power as a function of λ with f = 0.3 for different values of cp (g/l) as color indicates. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
31
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Fig. 5. The transmittance power as a function of λ with f = 0.5 for different values of cp (g/l) as color indicates. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
Fig. 6. The transmittance power as a function of λ with f = 0.7 for different values of cp (g/l) as color indicates. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
light through this layer,
⎡ cos(γi) Mi = ⎢ ⎢ ⎣− jpi sin(γi ) where, γi =
ω nd c i i
t=
−j sin(γi ) ⎤ pi
(10)
The transmittance power (T) is
⎥ cos(γi ) ⎦ ⎥
cos(θi ), c is the speed of light, pi =
2p0 (M11 + M12 p0 ) p0 + (M21 + M22 p0 )
(8)
T = |t|2
Equation (11) gives the study of transmission spectrum for the 1D ternary photonic crystal structures for the sensing applications while varying the blood plasma cell in the given defective region.
εi/ μi cos(θi ), μi is
permeability of i layer, cos(θi) = 1 − (n02/ ni2)sin2 (θ0) here θ0 is the angle of incidence. In the calculations, μi equals μ0 for air and θ0 = 0 for normal incidence. The total transfer matrix (M) for the entire structure surrounded by air is expressed by,
M M12 ⎤ M = ⎡ 11 = M0 (MA MB MC ) N MG MD MG (MA MB MC ) N M0 ⎢ M21 M22 ⎥ ⎣ ⎦
(11)
3. Results and discussion The calculation of transmission spectra of the proposed sensor is performed by Maple program. To optimize for the better sensing performance, two kinds of transmission calculation is carried out; First, the transmission power (T) is studied at different filling factor (f) of nanocomposites material while keeping the thickness of graphene layer dG as fixed. Secondly, the same calculation is repeated for changing in
(9)
Where M0 is for air, which surround the proposed structure. The transmittance coefficient (t) is defined as follows 32
Physica E: Low-dimensional Systems and Nanostructures 111 (2019) 29–36
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Fig. 7. The transmittance power as function of λ with f = 0.7 and dG = 20 nm for different values of cp (g/l) as color indicates. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
Fig. 8. The transmittance power as a function of λ with f = 0.7 and dG = 50 nm for different values of cp (g/l) as color indicates. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
values of the thickness of graphene layer dG by keeping filling factor (f) as fixed.
0.5, 0.7 and its corresponding spectral shift is plotted in blue, brown, green, yellow and red respectively. The overall plotting reveals that the effect of transmittance gets higher and higher while increasing filling factor which shows that the impact of silver particle provides the more absorption and reach for maximum values of transmittance at Cp = 0 g/ l as shown in Fig. 2. In similar way, the transmission calculation is repeated over the infrared region to detect the blood samples for different concentration for each filling factor (f = 0, 0.3, 0.5, 0.7) and the results are plotted as shown in Figs. 3–6 respectively. As the propagation belongs to defect modes in that forbidden gap, the overall transmission is exhibited the bell shaped curve. The curve characteristic is easily observed thus the maximum value of transmittance gives the equal energy transformation between the proposed ternary layers to the defective region. Each transmission shows distinct characteristics with respect to the wavelength and spectral wide. For example, the filling factor f = 0 case provides the different spectral shift
3.1. Determination of sensitivity with filling factor variation Fig. 2 shows the transmittance power as function of wavelength for the defective 1-D ternary photonic crystal when Cp = 0 g/l and dG = 34 nm at different values of f. It is noticed that the forbidden band expands to the left side of spectral region 750 nm to right side spectral region 1250 nm in which the mode propagation is cut off. Such that, TE propagation is significantly noted in the shortest range of wavelength band from 845 nm to 905 nm. The propagation modes describes that the presence of defect region in the middle structure with the coated graphene layer at both sides. For the case, if f = 0, nanocomposite layer is pure SiO2 and it exhibits that there is no prominent transmittance as sketched in block color curve. In a similar way, the filling factor values is increased as 0.2, 0.3, 0.4, 33
Physica E: Low-dimensional Systems and Nanostructures 111 (2019) 29–36
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Fig. 9. Variation of peak wavelength with function of blood plasma samples keeping f = 0.3, 0.5, 0.7.
Fig. 10. Variation of peak wavelength with function of blood plasma samples at graphene thickness.
other key point of Fig. 3 is that the normalized transmission values is sustained in the range of 0.16–0.18. The same analogy of transmission curve is taken into account for other filling factor cases. Fig. 4 shows the wavelength range of overall transmittance spectrum from 860 nm to 880 nm with the maximum peak transmission values of 0.25. Figs. 5 and 6 gives the overall spectral region as 870 nm–900 nm having maximum transmission value of 0.33 and 0.4 respectively. As a result, the analysis report specifies that the maximum peak transmittance with wider spectral shift is possible when the silver nanoparticle is more doped with SiO2 such that f = 0.7 in this case. The variation of the bandgap region is due to the coating of graphene layers which interacts in the energy variation for the TE mode propagation for the infrared region. Hence, the next sensing performance with respective transmission is analyzed for different thickness of graphene layers. The overall sensing performances and its value are
Table 1 Sensitivity values for the different concentration keeping f = 0.7and dG = 20 nm. Concentration g/l- refractive index
Peak wavelength (nm)
Sensitivity (nm/ [RIU])
10 g/l- 1.339692811 20 g/l- 1.359112811 30 g/l- 1.378532811 40 g/l- 1.397952811 50 g/l- 1.417372811
876.5 877.5 878 878.5 879
51.49 (from 10 to 20) 38.62 (from 10 to 30) 34.33 (from 10 to 40) 32.18 (from 10 to 50)
while defective region is considered for various concentration of plasma samples. The overall spectral region is covered from 840 nm to 870 nm where each concentration of plasma samples attains the peak point and its corresponding wavelength known as resonance wavelength. The 34
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calculations. Tables 1–3 show the step by step sensing performances. The reported values describe the potential of the proposed ternary structures sensor while varying the blood plasma cell from minimum to maximum of concentrations. As it inferred, the highest resonance wavelength is noted for dG = 50 nm. The overall calculation exhibits that the highest deviation of sensitivity is achieved for thickness of dG = 50 nm than the other case while varying the concentration plasma cell. Hence, the fabrication point of interest is inscribed in terms of it sensing performances as well as unique dimension of the proposed 1D ternary biosensor.
Table 2 Sensitivity values for the different concentration keeping f = 0.7and dG = 34 nm. Concentration g/l- refractive index
Peak wavelength (nm)
Sensitivity (nm/ [RIU])
10 g/l- 1.339692811 20 g/l- 1.359112811 30 g/l- 1.378532811 40 g/l- 1.397952811 50 g/l- 1.417372811
891.5 892.5 893 893.5 894.5
51.49 (from 10 to 20) 38.61 (from 10 to 30) 34.32 (from 10 to 40) 38.61 (from 10 to 50)
Table 3 Sensitivity values for the different concentration keeping f = 0.7and dG = 50 nm. Concentration g/l- refractive index
Peak wavelength (nm)
Sensitivity (nm/ [RIU])
10 g/l- 1.339692811 20 g/l- 1.359112811 30 g/l- 1.378532811 40 g/l- 1.397952811 50 g/l- 1.417372811
910.5 911 912 913 914
25.75 (from 10 to 20) 38.62 (from 10 to 30) 42.91 (from 10 to 40) 45.06 (from 10 to 50)
4. Conclusion In this work, we have introduced a refractive index sensor consisting of one dimensional ternary photonic crystal with defect layer for the blood plasma sensing applications. The defect layer is encapsulated between the graphene layers inserted at the middle of the photonic crystal to avoid any change in the property of original blood samples. The transmittance spectrum is tuned by using different factors such as the thickness of the graphene layer and the filling factor of Ag. It is noted that resonance shift has occurred whenever the plasma cell concentration has varied as 10 g/l, 20 g/l, 30 g/l, 40 g/l & 50 g/l in the given blood samples. The result shows that the sensor is functioning better with high filling factor than lower filling factor. It also give good results for both dG = 20 and 50 nm. Thus, we may recommend both for sensor fabrications. The calculation is performed using transfer matrix method (TMM). Maple is also used to numerically obtain the transmittance spectra.
reported in the preceding section. 3.2. The effect of the graphene thickness dG on the sensor performance As the previous transmission calculation is observed, the maximum peak point of transmittance with wider spectral shift for f = 0.7 and dG = 34 nm, the further transmittance studies are repeated for the different concentration (10 g/l to 50 g/l) of blood cell samples under the graphene layer thickness (dG), of 20 nm and 50 nm. The values are plotted as shown in Figs. 7 and 8. The interesting point in graphene layer thickness optimization is that the transmission spectrum gets wider and wider for the change in graphene layer thickness. For the previous case, Fig. 6 shows that bandgap region from 880 nm to 900 nm when dG = 34 nm. In Fig. 7, the transmission spectrum is calculated for the minimum of graphene layer thickness (dG = 20 nm) then it would be obvious that band gap region is lower in the range (860 nm–895 nm) than the case of dG = 34 nm. When it thickness reaches the 50 nm as shown in Fig. 8, the influence of graphene layer is more such that the band gap region is extended to the maximum wavelength point of 930 nm from its lower region point 890 nm. The other factor nothing but the peak values of spectrum for the different concentration of blood samples which get minimum peak point as graphene layer thickness is increased. It is clear that the wider spectrum has low transmittance power resulting low loss defect mode propagation with wider spectral shift.
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3.3. Sensitivity calculation and its analysis In the spectrum plots, the resonance peak wavelength occurring while varying the plasma blood samples for different filling factor and different graphene thickness is magnified and plotted as shown in Figs. 9 and 10. The difference between the changes of the resonance wavelength value (Δλ) of different Cp to the change of the corresponding refractive index (Δn) of plasma samples is known as sensitivity (S),
S=
Δλ Δn
(12)
The calculated sensitivity (S) at f = 0.7 for different values of Cp = 10 g/l, 20 g/l, 30 g/l, 40 g/l and 50 g/l and at dG = 20, 34, and 50 nm are summarized in Tables 1–3. The tabulation has also given the resonance wavelength point for the ease reference of sensitivity 35
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Physica E: Low-dimensional Systems and Nanostructures journal homepage: www.elsevier.com/locate/physe
Design of one dimensional refractive index sensor using ternary photonic crystal waveguide for plasma blood samples applications
T
Hala J. El-Khozondara, P. Mahalakshmib, Rifa J. El-Khozondarc, N.R. Ramanujamd, I.S. Amirie,f,∗, P. Yupapine a
Electrical Engineering Department, Islamic University of Gaza, Gaza, Palestine Department of Electronics and Communication, Vaigai College of Engineering, Madurai, 625 122, India c Physics Department, Al-Aqsa University, Gaza, Palestine d Department of Physics, K.L.N. College of Engineering, Pottapalayam, 630 612, India e Computational Optics Research Group, Advanced Institute of Materials Science, Ton Duc Thang University, Ho Chi Minh City, Viet Nam f Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Viet Nam b
A R T I C LE I N FO
A B S T R A C T
Keywords: Ternary PC Graphene Sensor Transfer matrix method (TMM)
One dimensional ternary photonic crystal based refractive index sensor is numerically proposed for the blood plasma sensing applications. It is achieved by introducing the defects or cavity cell, where the blood samples are infiltrated and surrounded by the graphene layers at the middle region of the ternary structures. Introduction of the graphene layer is to avoid the change in blood sample characteristics due to few ambient factors. The whole structure is then tuned to observe the transmittance spectrum over the infrared region (800 nm–1200 nm). It is noticed that the resonance spectral shift occurs for variation of the blood plasma samples as 10 g/l, 20 g/l, 30 g/l, 40 g/l & 50 g/l. These spectral shifts report the device sensitivity and it is optimized for different filling factor of nanocomposite material and different thickness of the graphene coating.
1. Introduction Optical sensors are important devices that detect and predict the signal changes in certain environments. They are useful in different applications, particularly, in industry and medicine. Their sensitivity depend on different factors including the type of materials, thickness of the film, and angle of incidence [1–4]. In earlier days, the properties of transfer matrix method (TMM) were investigated for different multilayered structures. It has been stacked and segmented as a different region by owning its refractive index which was also composited as one dimensional homogeneous multilayered thin film. In the case of structural formation with mirroring regions, the incident electromagnetic wave (EM) at a specific incidence angle hits the interface region and travels along the same stacked structure with the veneration of the materials properties. By 1950, the optical propagation characteristics of multilayered periodic region were evolved by using TMM [5]. Later it was verified by Hooke [6] and Newton et al. [7] during the pulse propagation in periodic multilayered regions with high dense of transmittance and reflectance over the band gap region which might be in visible, infrared, or mid-infrared regions [8]. Further, in order to tune up the efficient optical transmission characteristics, the
∗
composition of periodic multilayered structural pattern between the dielectric or any combination of materials was explored, where it is known as photonic crystal's (PCs) [9,10] which was also distended for 2D & 3D along with 1D [11–16]. The exertion of 1D-PC was proclaimed for the low intense of reflectivity by generating modes or photons as bands, where the region of zero propagation level for the periodic crystalline structure called as photonic band gap (PBG). Regardless the material composition and structural perfection, as the manipulation of the optical light can control the penetration, the photonic band gap analysis was extensively used in various applications and this features some fundamental physical studies such as filter applications especially for narrowband filter [17], bandpass filter [18], polarization controller [19], switching [20] and sensing applications [21,22]. Later it was inferred that the PBG effect also affectionate and enhancing the change of materials as well as the different structural module. In material aspects, PC's pulse propagation has been prolonged and proven in all kinds of dielectric region, nanocomposites region, plasma layer region [23–26] and superconductivity region [27]. Similarly, the band of the energy PCs response in its transmission and reflection spectrum for various structures, fibonacci quasi-periodic [28,29], graded multi-structure [30], thuemorse [31] and ternary structures [32]. In addition, the
Corresponding author. Ton Duc Thang University, Ho Chi Minh City, Viet Nam. E-mail address: [email protected] (I.S. Amiri).
https://doi.org/10.1016/j.physe.2019.02.030 Received 6 January 2019; Received in revised form 21 February 2019; Accepted 25 February 2019 Available online 28 February 2019 1386-9477/ © 2019 Elsevier B.V. All rights reserved.
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ternary based multilayer structures have some greater impacts on multi material composition properties for multi-applications especially it paid attention on sensing properties. Few researchers have been doing research on sensing in one dimensional [33] and two dimensional [34] PCs. More recently, researcher are fascinated by ternary photonic crystals due to their superior performance over one-dimensional periodic binary crystals in omni directional reflection [35], tunable optical filtering [36] and sensing applications [37]. In addition, the ternary structures are used for sensing application by forming the defect region [38] at the middle of the multilayered structure. Recently, JijiangWu et al. [39] proposed a temperature sensor using ternary structure in which one of the layers is superconductor material, where the sensor has reported sensitivity of 31.18 nm/K. In 2018, PCs had also been used for sensing devices in biomedical applications by Ramanujam et al. who proposed the refractive index sensor device for cancer cell by introducing defect layer with the exertion of mode function in the band gap region, where the device sensitivity was 43 nm/RIU [40]. In this article, the ternary based 1D photonic crystal is proposed for blood plasma sensing applications, where the sensing properties are tuned by adjusting the filling factor of the nanocomposites and the thickness of the graphene layers surrounded at both side region of the defective layer. In sensor development process, TMM is the time-saving in calculation and structure optimization. It can be also used for quickly design and optimizing the structure parameters. Next section is devoted to the design and theoretical background. Section 3 is dedicated to results and discussion followed by conclusion.
εAg = ε∞ −
εAg − εc εB − εc =f εB − 2εc εAg − 2εc
(2)
(3)
where, f is the Ag filling factor [45]. The period of the lattice is fixed as d = dA + dB + dC = 100 + 45 + 100 = 245 nm . The refractive index of the defected plasma in blood compound with the following formula
nD = 1.32459 + 0.001942Cp
(4)
where, Cp is the plasma concentration in blood and is measured in terms of g/l. In this calculation, Cp varies from 0 g/l to 50 g/l in steps of 10 g/l and its corresponding refractive index (nD) is calculated as 1.32459 to 1.42169. Since the graphene layers produce the low absorption at low frequency region and enhance the optical propagation characteristics in the infrared region, the defect layer is sandwiched in between the graphene nanolayers. It is due to influence the compact sensing properties during the process of variation of blood samples in g/l. The Graphene layer labeled as G has thickness dG and refractive index nG = εG with [46]
εG = 1 + j
σ (ω) ε0 ωd G
(5)
where, ε0 is the permittivity in the vacuum. σ(ω), the surface conductivity of graphene, equals σintra(ω) + σinter(ω), where σintra(ω)and σinter(ω) are intraband conductivity and the interband conductivity and is represented in the following expression
A 1-D ternary PC with defective layer is designed for detecting the plasma blood samples in the given blood analytes. As presented in Fig. 1, the proposed structure is Air/(SnS/Nanocomposite/SiO2)N/ Graphene/D/Graphene/(SnS/Nanocomposite/SiO2)N/Air. D is the defect layer to be filled with blood sample and the number of periods N is considered here as 5. Tin sulfide (SnS) is chosen as high-refractiveindex material with low transmittance in the optical frequency range of 500 nm to 3000 nm, where the SiO2 has been chosen as the low-refractive-index material and experimentally compact to form the thin layered film. The same SiO2 material is composited with silver nanoparticle by Maxwell garnett approximation to form the Nanocomposite material, which can be used to enhance the sensitivity in the given optical range. Further, the SnS layer thickness is dA = 100 nm, where its refractive index as nA is 2.6 [41]. The thickness and refractive index of the SiO2 layers are dC = 100 nm and nC = εC respectively and
0.61497λ2 − λ2c22 λ2 − c12
+ jωυp2
where, ω is the angular frequency, ωp is the selected plasma frequency which is taken as 9 eV, υp is the plasma collision frequency = 0.02eV and ε∞ is the permittivity at infinite frequencies (=5 for Ag). The Nanocomposite layer with thickness dB = 45 nm has effective index nB = εB where εB can be found from equation (3),
2. Design and theoretical background
εc = 1.4923 +
ωp2 ω2
σintra (ω) = −j
μc e 2kB T ⎛ μc + 2 ln ⎛e − kB T + 1⎞ ⎞⎟ ⎜ π ħ2 (ω − j Γ) ⎝ kB T ⎝ ⎠⎠
(6)
σinter (ω) = −j
2μ − (ω − j Γ)ħ ⎞ e2 ln ⎛⎜ c ⎟ 4π ħ ⎝ 2μc + (ω − j Γ)ħ ⎠
(7)
Where, e is the charge of an electron, μc is the chemical potential, Γ is the phenomenological scattering rate, T is the Kelvin temperature, kB is Boltzmann's constant, ħ = h/2π is the reduced Planck's constant. The graphene thickness dG is allowed to vary for the sack of optimizing the sensor characteristics. The overall sensing performance is numerically simulated for the proposed structure for the TE mode propagation in the infrared region. For the TE modes, transfer matrix method (TMM) is used to study the interaction of light through the structural penetration of photonic crystal in the optical region and it also could be possible for experimental validation while following the one dimensional multilayer practical measurement [47–49]. For the periodic layer i, the matrix Mi describe the propagation of
(1) −2
and λ is the wavelength where, C1 = 0.115 μm, C2 = 0.01059 μm [42]. For unmagnetized plasma, the frequency dependent dielectric permittivity for silver (εAg) meets the Drude model and it can be written as [43,44]:
Fig. 1. The proposed 1-D ternary PC sensor. 30
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Fig. 2. The transmittance power as a function of λ for cp = 0 g/l at different values of f as indicated.
Fig. 3. The transmittance power as a function of λ for different values of cp (g/l) as color indicates at f = 0. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
Fig. 4. The transmittance power as a function of λ with f = 0.3 for different values of cp (g/l) as color indicates. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
31
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Fig. 5. The transmittance power as a function of λ with f = 0.5 for different values of cp (g/l) as color indicates. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
Fig. 6. The transmittance power as a function of λ with f = 0.7 for different values of cp (g/l) as color indicates. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
light through this layer,
⎡ cos(γi) Mi = ⎢ ⎢ ⎣− jpi sin(γi ) where, γi =
ω nd c i i
t=
−j sin(γi ) ⎤ pi
(10)
The transmittance power (T) is
⎥ cos(γi ) ⎦ ⎥
cos(θi ), c is the speed of light, pi =
2p0 (M11 + M12 p0 ) p0 + (M21 + M22 p0 )
(8)
T = |t|2
Equation (11) gives the study of transmission spectrum for the 1D ternary photonic crystal structures for the sensing applications while varying the blood plasma cell in the given defective region.
εi/ μi cos(θi ), μi is
permeability of i layer, cos(θi) = 1 − (n02/ ni2)sin2 (θ0) here θ0 is the angle of incidence. In the calculations, μi equals μ0 for air and θ0 = 0 for normal incidence. The total transfer matrix (M) for the entire structure surrounded by air is expressed by,
M M12 ⎤ M = ⎡ 11 = M0 (MA MB MC ) N MG MD MG (MA MB MC ) N M0 ⎢ M21 M22 ⎥ ⎣ ⎦
(11)
3. Results and discussion The calculation of transmission spectra of the proposed sensor is performed by Maple program. To optimize for the better sensing performance, two kinds of transmission calculation is carried out; First, the transmission power (T) is studied at different filling factor (f) of nanocomposites material while keeping the thickness of graphene layer dG as fixed. Secondly, the same calculation is repeated for changing in
(9)
Where M0 is for air, which surround the proposed structure. The transmittance coefficient (t) is defined as follows 32
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Fig. 7. The transmittance power as function of λ with f = 0.7 and dG = 20 nm for different values of cp (g/l) as color indicates. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
Fig. 8. The transmittance power as a function of λ with f = 0.7 and dG = 50 nm for different values of cp (g/l) as color indicates. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
values of the thickness of graphene layer dG by keeping filling factor (f) as fixed.
0.5, 0.7 and its corresponding spectral shift is plotted in blue, brown, green, yellow and red respectively. The overall plotting reveals that the effect of transmittance gets higher and higher while increasing filling factor which shows that the impact of silver particle provides the more absorption and reach for maximum values of transmittance at Cp = 0 g/ l as shown in Fig. 2. In similar way, the transmission calculation is repeated over the infrared region to detect the blood samples for different concentration for each filling factor (f = 0, 0.3, 0.5, 0.7) and the results are plotted as shown in Figs. 3–6 respectively. As the propagation belongs to defect modes in that forbidden gap, the overall transmission is exhibited the bell shaped curve. The curve characteristic is easily observed thus the maximum value of transmittance gives the equal energy transformation between the proposed ternary layers to the defective region. Each transmission shows distinct characteristics with respect to the wavelength and spectral wide. For example, the filling factor f = 0 case provides the different spectral shift
3.1. Determination of sensitivity with filling factor variation Fig. 2 shows the transmittance power as function of wavelength for the defective 1-D ternary photonic crystal when Cp = 0 g/l and dG = 34 nm at different values of f. It is noticed that the forbidden band expands to the left side of spectral region 750 nm to right side spectral region 1250 nm in which the mode propagation is cut off. Such that, TE propagation is significantly noted in the shortest range of wavelength band from 845 nm to 905 nm. The propagation modes describes that the presence of defect region in the middle structure with the coated graphene layer at both sides. For the case, if f = 0, nanocomposite layer is pure SiO2 and it exhibits that there is no prominent transmittance as sketched in block color curve. In a similar way, the filling factor values is increased as 0.2, 0.3, 0.4, 33
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Fig. 9. Variation of peak wavelength with function of blood plasma samples keeping f = 0.3, 0.5, 0.7.
Fig. 10. Variation of peak wavelength with function of blood plasma samples at graphene thickness.
other key point of Fig. 3 is that the normalized transmission values is sustained in the range of 0.16–0.18. The same analogy of transmission curve is taken into account for other filling factor cases. Fig. 4 shows the wavelength range of overall transmittance spectrum from 860 nm to 880 nm with the maximum peak transmission values of 0.25. Figs. 5 and 6 gives the overall spectral region as 870 nm–900 nm having maximum transmission value of 0.33 and 0.4 respectively. As a result, the analysis report specifies that the maximum peak transmittance with wider spectral shift is possible when the silver nanoparticle is more doped with SiO2 such that f = 0.7 in this case. The variation of the bandgap region is due to the coating of graphene layers which interacts in the energy variation for the TE mode propagation for the infrared region. Hence, the next sensing performance with respective transmission is analyzed for different thickness of graphene layers. The overall sensing performances and its value are
Table 1 Sensitivity values for the different concentration keeping f = 0.7and dG = 20 nm. Concentration g/l- refractive index
Peak wavelength (nm)
Sensitivity (nm/ [RIU])
10 g/l- 1.339692811 20 g/l- 1.359112811 30 g/l- 1.378532811 40 g/l- 1.397952811 50 g/l- 1.417372811
876.5 877.5 878 878.5 879
51.49 (from 10 to 20) 38.62 (from 10 to 30) 34.33 (from 10 to 40) 32.18 (from 10 to 50)
while defective region is considered for various concentration of plasma samples. The overall spectral region is covered from 840 nm to 870 nm where each concentration of plasma samples attains the peak point and its corresponding wavelength known as resonance wavelength. The 34
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calculations. Tables 1–3 show the step by step sensing performances. The reported values describe the potential of the proposed ternary structures sensor while varying the blood plasma cell from minimum to maximum of concentrations. As it inferred, the highest resonance wavelength is noted for dG = 50 nm. The overall calculation exhibits that the highest deviation of sensitivity is achieved for thickness of dG = 50 nm than the other case while varying the concentration plasma cell. Hence, the fabrication point of interest is inscribed in terms of it sensing performances as well as unique dimension of the proposed 1D ternary biosensor.
Table 2 Sensitivity values for the different concentration keeping f = 0.7and dG = 34 nm. Concentration g/l- refractive index
Peak wavelength (nm)
Sensitivity (nm/ [RIU])
10 g/l- 1.339692811 20 g/l- 1.359112811 30 g/l- 1.378532811 40 g/l- 1.397952811 50 g/l- 1.417372811
891.5 892.5 893 893.5 894.5
51.49 (from 10 to 20) 38.61 (from 10 to 30) 34.32 (from 10 to 40) 38.61 (from 10 to 50)
Table 3 Sensitivity values for the different concentration keeping f = 0.7and dG = 50 nm. Concentration g/l- refractive index
Peak wavelength (nm)
Sensitivity (nm/ [RIU])
10 g/l- 1.339692811 20 g/l- 1.359112811 30 g/l- 1.378532811 40 g/l- 1.397952811 50 g/l- 1.417372811
910.5 911 912 913 914
25.75 (from 10 to 20) 38.62 (from 10 to 30) 42.91 (from 10 to 40) 45.06 (from 10 to 50)
4. Conclusion In this work, we have introduced a refractive index sensor consisting of one dimensional ternary photonic crystal with defect layer for the blood plasma sensing applications. The defect layer is encapsulated between the graphene layers inserted at the middle of the photonic crystal to avoid any change in the property of original blood samples. The transmittance spectrum is tuned by using different factors such as the thickness of the graphene layer and the filling factor of Ag. It is noted that resonance shift has occurred whenever the plasma cell concentration has varied as 10 g/l, 20 g/l, 30 g/l, 40 g/l & 50 g/l in the given blood samples. The result shows that the sensor is functioning better with high filling factor than lower filling factor. It also give good results for both dG = 20 and 50 nm. Thus, we may recommend both for sensor fabrications. The calculation is performed using transfer matrix method (TMM). Maple is also used to numerically obtain the transmittance spectra.
reported in the preceding section. 3.2. The effect of the graphene thickness dG on the sensor performance As the previous transmission calculation is observed, the maximum peak point of transmittance with wider spectral shift for f = 0.7 and dG = 34 nm, the further transmittance studies are repeated for the different concentration (10 g/l to 50 g/l) of blood cell samples under the graphene layer thickness (dG), of 20 nm and 50 nm. The values are plotted as shown in Figs. 7 and 8. The interesting point in graphene layer thickness optimization is that the transmission spectrum gets wider and wider for the change in graphene layer thickness. For the previous case, Fig. 6 shows that bandgap region from 880 nm to 900 nm when dG = 34 nm. In Fig. 7, the transmission spectrum is calculated for the minimum of graphene layer thickness (dG = 20 nm) then it would be obvious that band gap region is lower in the range (860 nm–895 nm) than the case of dG = 34 nm. When it thickness reaches the 50 nm as shown in Fig. 8, the influence of graphene layer is more such that the band gap region is extended to the maximum wavelength point of 930 nm from its lower region point 890 nm. The other factor nothing but the peak values of spectrum for the different concentration of blood samples which get minimum peak point as graphene layer thickness is increased. It is clear that the wider spectrum has low transmittance power resulting low loss defect mode propagation with wider spectral shift.
Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.physe.2019.02.030. References [1] H.J. El-Khozondar, M. Shabat, Rana Khlifa, Sensitivity enhancement of nonlinear waveguide sensors with conducting graphene layer: TE mode, Photonic Sensors 8 (2018) 29–3. [2] H.J. El-Khozondar, R.J. El-Khozondar, M.M. Shabat, Dispersion characteristics and sensitivity properties of Graphene surface Plasmon sensor, Sens. Lett. 15 (2017) 249–252. [3] R.J. El-Khozondar, H.J. El-Khozondar, M.M. Shabat, Enhancing sensor sensitivity using Graphene-MTM interface, Am. J. Nano Res. Appl. 4 (2016) 43–46. [4] H.J. El-Khozondar, Z.I. Al-Sahhar, M.M. Shabat, The sensitivity of Surface Polaritons in LHM-antiferromagnetic waveguide sensors, J. Magn. Magn Mater. 368 (2014) 312–317. [5] F. Abelès, Recherches sur la propagation des ondes électromagnétiques sinusoïdales dans les milieux stratifies: application aux couches minces, Ann. Phys. 12 (1950) 596–640. [6] R. Hooke, Micrographia, The Royal Society, London, 1665. Reprinted By Palo Alto: Octavo (1998), ISBN 1891788027. [7] I. Newton, Opticks, fourth ed., William Innys, London, 1730. Reprinted By New York: Dover Publications (1952), ISBN 486602052. [8] M. Shabat, H.J. El-Khozondar, A.N. AlSembari, R.J. El-Khozondar, Transfer matrix method application on semiconductor based solar cell characteristics measurements, J. Mod. Phys. B 32 (2018) 1850346. [9] E. Yablanovitch, Inhibited spontaneous emission in solid state physics and electronics, Phys. Rev. Lett. 58 (1987) 2059. [10] S. John, Localization of light, Phys. Rev. Lett. 58 (1987) 2486. [11] J.D. Joannopoulos, S.G. Johnson, J.N. Winn, R.D. Meade, Photonic Crystals: Molding the Flow of Light, Princeton University Press, Princeton, NJ, USA, 2008. [12] H.A. Elsayed, S.A. El-Naggar, A.H. Aly, Two dimensional tunable photonic crystals and N doped semiconductor materials, Mater. Chem. Phys. 160 (2015) 221–226. [13] Y. Fink, J.N. Winn, F. Shanhui, C. Chiping, J. Michel, J.D. Joannopoulos, E.L. Thomas, A dielec-tric omnidirectional reflector, Science 282 (1998) 1679–1682. [14] A.H. Aly, H.A. Elsayed, S.A. El-Naggar, Tuning the flow of light in two-dimensional metallic photonic crystals based on Faraday effect, J. Mod. Optic. 64 (2017) 74–80. [15] A.H. Aly, D. Mohamed, BSCCO/SrTiO3 one dimensional superconducting photonic crystal for many applications, J. Supercond. Nov. Magn. 28 (2015) 1699–1703. [16] D.R. Smith, R. Dalichaouch, N. Kroll, S. Schultz, S.L. Mccall, P.M. Platzman, Photonic band structure and defects in one and two dimensions, J. Opt. Soc. Am. B
3.3. Sensitivity calculation and its analysis In the spectrum plots, the resonance peak wavelength occurring while varying the plasma blood samples for different filling factor and different graphene thickness is magnified and plotted as shown in Figs. 9 and 10. The difference between the changes of the resonance wavelength value (Δλ) of different Cp to the change of the corresponding refractive index (Δn) of plasma samples is known as sensitivity (S),
S=
Δλ Δn
(12)
The calculated sensitivity (S) at f = 0.7 for different values of Cp = 10 g/l, 20 g/l, 30 g/l, 40 g/l and 50 g/l and at dG = 20, 34, and 50 nm are summarized in Tables 1–3. The tabulation has also given the resonance wavelength point for the ease reference of sensitivity 35
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